To solve the equation \( x^8 - 5 = -3 \), we first add 5 to both sides:
\[ x^8 - 5 + 5 = -3 + 5 \]
This simplifies to:
\[ x^8 = 2 \]
Next, to solve for \( x \), we take the eighth root of both sides:
\[ x = \pm 2^{1/8} \]
Since \( 2^{1/8} \) is a positive value, we only need to find the numerical approximate. However, none of the provided answer choices (-64, 1, -16, 16) are equivalent to \( 2^{1/8} \) or \( -2^{1/8} \).
Let’s analyze what these answers represent as potential values for \( x \):
- \( -64 \): \( (-64)^8 \neq 2 \)
- \( 1 \): \( (1)^8 = 1 \) (not a solution)
- \( -16 \): \( (-16)^8 \neq 2 \)
- \( 16 \): \( (16)^8 \neq 2 \)
Therefore, none of these choices are correct solutions based on the calculation.
Given the context of your question, if we need to evaluate numerically:
The closest numerical approximation of \( 2^{1/8} \) is about \( 1.0905 \). Since this value is not directly given in the choices, and since \( 1 \) is the closest provided option, one might consider choosing \( 1 \) for the purposes of a multiple choice activity, although strictly speaking it is not a correct solution.
So, the answer is:
1 (approximately), though it’s important to note it is not an exact solution to \( x^8 = 2 \).
1 answer